Set-Valued Analysis"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject." —Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math |
From inside the book
Results 1-5 of 79
... Compact Sets .... 365 9.4.2 The Intersection Lemma 369 9.4.3 Lipschitz Selections of Lipschitz Maps 372 9.5 Selections of Caratheodory maps 373 9.6 Caratheodory Parametrization 376 9.7 Measurable/Lipschitz Parametrization 379 10 ...
... compact set are upper semicontinuous. Hence we have an easy way to verify upper semicontinuity of a map. Lower semicontinuity is not as simple to check: the last section is devoted to several useful lower semicontinuity criteria. The ...
... compact, each neighborhood of K contains such a ball around K. Limits of sets have been introduced by Painleve3 in 1902, as it is reported by his student Zoretti4. They have been popularized by Kuratowski in his famous book Topologie ...
... compact if and only if every generalized sequence of elements of K has a cluster point. (See for instance [148, Section 1.7].) The main difference with sequences of a metric space is that a converging generalized sequence is not ...
... compact. However, in general X is a closed subspace of the bidual X** of X, which is the dual of the Banach space X*, endowed with the norm ||p||* := sup | <p,x > | IWI<i The space X is called reflexive if X = X**. In this case, it ...